George has a total of B books in his library

[jjjinapinch]

George has a total of B books in his library, 25 of which are hardcover fiction books. What is the value of B?

(1) 40 of the B books are fiction and the rest are nonfiction
(2) 60 of the B books are hardcovers and the rest are paperbacks

Official Guide question
Answer: E

[Jay@ManhattanReview]

George has a total of B books in his library, 25 of which are hardcover fiction books. What is the value of B?

(1) 40 of the B books are fiction and the rest are nonfiction
(2) 60 of the B books are hardcovers and the rest are paperbacks

Official Guide question
Answer: E

We have the total number of books = B;

Say,
Number of Hardcover books = H;
Number of Hardcover Fiction books = HF;
Number of Hardcover Non-fiction books = HNF;

Number of Paperback books = P;
Number of Paperback Fiction books = PF;
Number of Paperback Non-fiction books = PNF

Thus,
B = H + P ---(1)

B = [HF + HNF] + [PF + PNF] ---(2)

B = [25 + HNF] + [PF + PNF] ---(2)

We have to get the value of B.

Statement 1: 40 of the B books are fiction and the rest are nonfiction.

=> HF + PF = 40 and HNF + PNF = B - 40
=> PF = 40 - 25 = 15

From eqn (2), we have

B = [25 + HNF] + [15 + PNF] ---(2)
B = 40 + HNF + PNF
B = 40 + B - 40
B = B. Can't get B. Insufficient.

Statement 2: 60 of the B books are hardcovers and the rest are paperbacks.

=> H = 60 => H = HF + HNF => 60 = 25 + HNF => HNF = 35

From eqn (1), we have

B = H + P ---(1)

B = 40 + P. We do not know the value of P. Insufficient.

Statement 1 and 2:

Even after combining both the statement, we cannot get the value of PNF, thus the value of B. Insufficient.

The correct answer: E

Hope this helps!

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-Jay
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Hi All,

We're told that George has a total of B books in his library, 25 of which are HARDCOVER FICTION books. We're asked for the value of B. Based on the information given so far, it's likely that there will be hardcover and 'not' hardcover (meaning 'paperback') books as well as fiction and 'not' fiction (meaning 'nonfiction) books. This implies that there are many variables to keep track of - and we'll need a LOT of specific information for either Fact to be considered Sufficient.

1) 40 of the B books are fiction and the rest are nonfiction

With Fact 1, we now know that 40 of the books are FICTION (which includes the 25 that are HARDCOVER FICTION). Thus, there are 40 - 25 = 15 paperback fiction books, but we still don't know how many non-fiction books there are (of either type).
Fact 1 is INSUFFICIENT

2) 60 of the B books are hardcovers and the rest are paperbacks

With Fact 2, we now know that 60 of the books are HARDCOVER (which includes the 25 that are HARDCOVER FICTION). Thus, there are 60 - 25 = 35 hardcover nonfiction books, but we still don't know how many paperback books there are (of either type).
Fact 2 is INSUFFICIENT

Combined, we know there are...
25 Hardcover Fiction books
15 Paperback Fiction books
35 Hardcover Non-Fiction books
X Paperback Non-Fiction books

Since we don't know the number of Paperback Non-Fiction books, there's not enough information to answer the question.
Combined, INSUFFICIENT.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

George has a total of B books in his library, 25 of which are hardcover fiction books. What is the value of B?

(1) 40 of the B books are fiction and the rest are nonfiction
(2) 60 of the B books are hardcovers and the rest are paperbacks

Official Guide question
Answer: E

Solution:

Question Stem Analysis:

We need to determine the value of B, the number of books in George’s library. (Note: Here we are assuming all the books in George are either fiction or nonfiction, and either hardcover or paperback.)

Statement One Alone:

Since 40 books are fiction books and 25 are hardcover fiction books, 40 - 25 = 15 books are paperback fiction books. However, we can’t determine the value of B, the number of books in George’s library. Statement one alone is not sufficient.

Statement Two Alone:

Since 60 books are hardcovers and 25 are hardcover fiction books, 60 - 25 = 35 books are hardcover nonfiction books. However, we can’t determine the value of B, the number of books in George’s library. Statement two alone is not sufficient.

Statements One and Two Together:

From the two statements, we can see that there are 25 hardcover fiction books, 15 paperback fiction books, and 35 hardcover nonfiction books. However, since we still don’t know the number of paperback nonfiction books, we can’t determine the value of B, the number of books in George’s library. Both statements together are still not sufficient.

Answer: E